2.4 fsva for prediction

For genomic prediction, datasets are generally composed of a training set and a test set. For each sample in the training set, the outcome/class is known, but latent sources of variability are unknown. For the samples in the test set, neither the outcome/class nor the latent sources of variability are known. When applying genomic predictors, individual samples must be corrected. But most functions for batch correction and surrogate variable estimation have been developed in the context of population studies. ‘Frozen’ surrogate variable analysis can be used to remove latent variation in the training and test sets, as well as individual samples obtained in future studies, similar to the recently developed normalization procedures (McCall et al., 2010).

The arguments that must be passed to fsva are a database of measurements from the training set (dbdat), the model matrix for the training set (mod), the sva object obtained from running sva on the training set and optionally the data from the test set (newdat). The fsva function returns corrected training data (db) and corrected test data (new). If new samples are obtained, they can be adjusted for surrogate variables by including them in the newdat data matrix while leaving all other arguments the same. To illustrate this method, we applied the fsva function to a previously published study of gene expression in bladder cancer. Adjustment with fsva led to increased accuracy and improved clustering of samples in the test set (Supplemental Materials).

3.1 Surrogate variables versus direct adjustment

The goal of sva is to remove all unwanted sources of variation while protecting the contrasts due to the primary variables specified in the function call. This leads to the identification of features that are consistently different between groups, removing all common sources of latent variation.

In some cases, latent variables may be important sources of biological variability. If the goal of the analysis is to identify heterogeneity in one or more subgroups, the sva function may not be appropriate. For example, suppose it is expected that cancer samples represent two distinct, but unknown subgroups of biological interest. If these subgroups have a large impact on expression, then one or more of the estimated surrogate variables may be highly correlated with the subgroup (Teschendorff et al., 2011). This is true regardless of whether the surrogate variables are estimated with principal components, singular vectors (Leek and Storey, 2007, 2008) or independent components (Teschendorff et al., 2011). However, removing surrogate variables that are correlated with the phenotype of interest may lead to inconsistent and anti-conservatively biased significance analysis, specially if unknown latent variables are correlated with the phenotype of interest (Leek and Storey, 2007). Thus, whether exclusion of surrogate variables improves inference or not is an open unsolved problem.

In contrast, direct adjustment only removes the effect of known batch variables. Batch effects are the best-known source of latent variation in genomic experiments (Leek et al., 2010). However, there are many variables that may have a substantial impact on genomic measurements, from environmental variables (Gibson, 2008) to genetic variation (Brem et al., 2002; Schadt et al., 2003). These variables may be the focus of the study being performed. But there are many studies that focus on identifying the association between genomic measurements and specific outcomes or phenotypes. In these studies, genetic and environmental variables are often unmeasured or unmodeled. If ignored, these biological variables may act in the same way that batch effects act by obscuring signal, reducing power and biasing biological conclusions (Leek and Storey, 2007).

As a rule of thumb, when there are a large number of known or unknown potential confounders, surrogate variable adjustment may be more appropriate. Alternatively, when one or more biological groups is known to be heterogeneous, and there are known batch variables, direct adjustment may be more appropriate.